Chapter 4

Report
Chapter 4
Gates and Circuits
Chapter Goals
• Identify the basic gates and describe the
behavior of each
• Describe how gates are implemented
using transistors
• Combine basic gates into circuits
• Describe the behavior of a gate or circuit
using Boolean expressions, truth tables,
and logic diagrams
2
Chapter Goals
• Compare and contrast a half adder
and a full adder
• Describe how a multiplexer works
• Explain how an S-R latch operates
• Describe the characteristics of the four
generations of integrated circuits
3
Computers and Electricity
Gate
A device that performs a basic operation on
electrical signals
Circuits
Gates combined to perform more
complicated tasks
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Computers and Electricity
How do we describe the behavior of gates and
circuits?
Boolean expressions
Uses Boolean algebra, a mathematical notation for
expressing two-valued logic
Logic diagrams
A graphical representation of a circuit; each gate has its
own symbol
Truth tables
A table showing all possible input value and the associated
output values
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Gates
Six types of gates
–
–
–
–
–
–
NOT
AND
OR
XOR
NAND
NOR
Typically, logic diagrams are black and white with
gates distinguished only by their shape
We use color for emphasis (and fun)
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NOT Gate
A NOT gate accepts one input signal (0 or 1) and
returns the opposite signal as output
Figure 4.1 Various representations of a NOT gate
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AND Gate
An AND gate accepts two input signals
If both are 1, the output is 1; otherwise,
the output is 0
Figure 4.2 Various representations of an AND gate
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OR Gate
An OR gate accepts two input signals
If both are 0, the output is 0; otherwise,
the output is 1
Figure 4.3 Various representations of a OR gate
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XOR Gate
An XOR gate accepts two input signals
If both are the same, the output is 0; otherwise,
the output is 1
Figure 4.4 Various representations of an XOR gate
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XOR Gate
Note the difference between the XOR gate
and the OR gate; they differ only in one
input situation
When both input signals are 1, the OR gate
produces a 1 and the XOR produces a 0
XOR is called the exclusive OR
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NAND Gate
The NAND gate accepts two input signals
If both are 1, the output is 0; otherwise,
the output is 1
Figure 4.5 Various representations of a NAND gate
NOR Gate
The NOR gate accepts two input signals
If both are 0, the output is 1; otherwise,
the output is 0
Figure 4.6 Various representations of a NOR gate
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Review of Gate Processing
A NOT gate inverts its single input
An AND gate produces 1 if both input values are 1
An OR gate produces 0 if both input values are 0
An XOR gate produces 0 if input values are the
same
A NAND gate produces 0 if both inputs are 1
A NOR gate produces a 1 if both inputs are 0
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Gates with More Inputs
Gates can be designed to accept three or more input
values
A three-input AND gate, for example, produces an output of
1 only if all input values are 1
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Figure 4.7 Various representations of a three-input AND gate
Constructing Gates
Transistor
A device that acts either as a wire that conducts
electricity or as a resistor that blocks the flow of
electricity, depending on the voltage level of an
input signal
A transistor has no moving parts, yet acts like
a switch
It is made of a semiconductor material, which is
neither a particularly good conductor of electricity
nor a particularly good insulator
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Constructing Gates
A transistor has three terminals
– A source
– A base
– An emitter, typically
connected to a ground wire
If the electrical signal is
grounded, it is allowed to flow
through an alternative route to
the ground (literally) where it
can do no harm
Figure 4.8 The connections of a transistor
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Constructing Gates
The easiest gates to create are the NOT, NAND,
and NOR gates
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Figure 4.9 Constructing gates using transistors
Circuits
Combinational circuit
The input values explicitly determine the output
Sequential circuit
The output is a function of the input values and the
existing state of the circuit
We describe the circuit operations using
Boolean expressions
Logic diagrams
Truth tables
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Are you surprised?
Combinational Circuits
Gates are combined into circuits by using the
output of one gate as the input for another
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Combinational Circuits
Three inputs require eight rows to describe all possible
input combinations
This same circuit using a Boolean expression is (AB + AC)
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Combinational Circuits
Consider the following Boolean expression A(B + C)
Does this truth table look familiar?
Compare it with previous table
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Combinational Circuits
Circuit equivalence
Two circuits that produce the same output for
identical input
Boolean algebra allows us to apply provable
mathematical principles to help design circuits
A(B + C) = AB + BC (distributive law) so circuits
must be equivalent
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Properties of Boolean
Algebra
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Adders
At the digital logic level, addition is
performed in binary
Addition operations are carried out
by special circuits called, appropriately,
adders
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Adders
The result of adding two
binary digits could
produce a carry value
Recall that 1 + 1 = 10
in base two
Half adder
A circuit that computes
the sum of two bits
and produces the correct
carry bit
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Truth table
Adders
Circuit diagram
representing
a half adder
Boolean expressions
sum = A  B
carry = AB
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Adders
Full adder
A circuit that takes the carry-in value into account
Figure 4.10 A full adder
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Multiplexers
Multiplexer
A circuit that uses a few input control signals
to determine which of several output data
lines is routed to its output
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Multiplexers
Figure 4.11 A block diagram of a multiplexer with three
select control lines
The control lines
S0, S1, and S2
determine which
of eight other
input lines
(D0 … D7)
are routed to the
output (F)
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Circuits as Memory
Digital circuits can be used to store
information
These circuits form a sequential circuit,
because the output of the circuit is also used
as input to the circuit
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Circuits as Memory
An S-R latch stores a
single binary digit
(1 or 0)
There are several
ways an S-R latch
circuit can be
designed using
various kinds of gates
Figure 4.12 An S-R latch
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Circuits as Memory
The design of this circuit
guarantees that the two outputs
X and Y are always
complements of each other
The value of X at any point in
time is considered to be the
current state of the circuit
Therefore, if X is 1, the circuit is
storing a 1; if X is 0, the circuit is
storing a 0
Figure 4.12 An S-R latch
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Integrated Circuits
Integrated circuit (also called a chip)
A piece of silicon on which multiple gates
have been embedded
Silicon pieces are mounted on a plastic or
ceramic package with pins along the edges
that can be soldered onto circuit boards or
inserted into appropriate sockets
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Integrated Circuits
Integrated circuits (IC) are classified by the
number of gates contained in them
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Integrated Circuits
Figure 4.13 An SSI chip contains independent NAND gates
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CPU Chips
The most important integrated circuit
in any computer is the Central Processing
Unit, or CPU
Each CPU chip has a large number of pins
through which essentially all communication
in a computer system occurs
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Ethical Issues
Email Privacy
Explain why privacy is an illusion.
Who can read your email?
Do you send personal email from
work?
Does everyone in your family use
email?
38
Who am I?
All the world knows my name. What is
it and why do people know it?
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Do you know?
What is the name of the study of materials
smaller than 100 nanometers?
Did DeMorgan discover DeMorgan's laws?
How do archeologists use GPS systems?
What's wrong with uploading your photos
to a social networking site?
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